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# Four friends Laura, Nancy, James and Simon buy some pencils,

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Intern
Joined: 16 Aug 2013
Posts: 7

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Updated on: 20 Aug 2013, 02:07
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Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 10 sessions

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Four friends Laura, Nancy, James and Simon buy some pencils, pens and erasers from a shop. Laura buys 5 pencils, 6 pens, and 1 eraser for \$17.50. Nancy buts 3 pens, 3 pencils, and 2 erasers for \$ 10. James buys 5 pens, 2 pencils, and 5 erasers for \$14.50. How much will Simon have to pay if he buys 3 pens, 2 pencils, and 5 erasers?

Note: How often in the GMAT do such questions appear?
Can i have a generic way to solve such questions?

OA:
\$9.5

Originally posted by vinayparamanand on 19 Aug 2013, 20:13.
Last edited by Bunuel on 20 Aug 2013, 02:07, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 21 Aug 2012
Posts: 120

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20 Aug 2013, 01:14
vinayparamanand wrote:
Four friends Laura, Nancy, James and Simon buy some pencils, pens and erasers from a shop. Laura buys 5 pencils, 6 pens, and 1 eraser for \$17.50. Nancy buts 3 pens, 3 pencils, and 2 erasers for \$ 10. James buys 5 pens, 2 pencils, and 5 erasers for \$14.50. How much will Simon have to pay if he buys 3 pens, 2 pencils, and 5 erasers?

Note: How often in the GMAT do such questions appear?
Can i have a generic way to solve such questions?

A: \$9.5

Let the cost of a pencil be \$x
Let the cost of a pen be \$y
Let the cost of a erasers be \$z

Now,
for Laura 5x+6y+z = 17.50 ----a
for Nancy 3x+3y+2z=10 ----b
for James 2x+5y+5z=14.50 ---c

We have to find value for Simon i.e 3x+2y+5z=??

Now,
2b - a => x + 3z = 2.5 ----d
5b - 3c => 9x - 5z = 6.5 ------e

Solving, d and e

9d - e => 9x + 27z - (9x-5z ) = 22.5 - 6.5
32z = 16
z = 1/2

putting z in d, we get x = 1
putting z and x in a we get y= 2

3x + 2y +5z = 3 + 4 + 2.5 => 9.5\$

Thanks,
Jai

KUDOS if it HELPED..!!!
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MODULUS Concept ---> http://gmatclub.com/forum/inequalities-158054.html#p1257636
HEXAGON Theory ---> http://gmatclub.com/forum/hexagon-theory-tips-to-solve-any-heaxgon-question-158189.html#p1258308

Intern
Joined: 22 Feb 2010
Posts: 42

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01 Sep 2013, 11:56
I agree with the solution provided here, but I would like to know an alternative way that is easier and can be done in the shortest amount of time possible. The current approach is lengthy and time-consuming.
Thanks.
jaituteja wrote:
vinayparamanand wrote:
Four friends Laura, Nancy, James and Simon buy some pencils, pens and erasers from a shop. Laura buys 5 pencils, 6 pens, and 1 eraser for \$17.50. Nancy buts 3 pens, 3 pencils, and 2 erasers for \$ 10. James buys 5 pens, 2 pencils, and 5 erasers for \$14.50. How much will Simon have to pay if he buys 3 pens, 2 pencils, and 5 erasers?

Note: How often in the GMAT do such questions appear?
Can i have a generic way to solve such questions?

A: \$9.5

Let the cost of a pencil be \$x
Let the cost of a pen be \$y
Let the cost of a erasers be \$z

Now,
for Laura 5x+6y+z = 17.50 ----a
for Nancy 3x+3y+2z=10 ----b
for James 2x+5y+5z=14.50 ---c

We have to find value for Simon i.e 3x+2y+5z=??

Now,
2b - a => x + 3z = 2.5 ----d
5b - 3c => 9x - 5z = 6.5 ------e

Solving, d and e

9d - e => 9x + 27z - (9x-5z ) = 22.5 - 6.5
32z = 16
z = 1/2

putting z in d, we get x = 1
putting z and x in a we get y= 2

3x + 2y +5z = 3 + 4 + 2.5 => 9.5\$

Thanks,
Jai

KUDOS if it HELPED..!!!
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Joined: 09 Sep 2013
Posts: 8153
Re: Four friends Laura, Nancy, James and Simon buy some pencils,  [#permalink]

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26 Sep 2017, 04:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Four friends Laura, Nancy, James and Simon buy some pencils, &nbs [#permalink] 26 Sep 2017, 04:24
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# Four friends Laura, Nancy, James and Simon buy some pencils,

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